Question

HEYA!!!

Find 6 rational numbers between 5 and 7 using suitable formula.

No spamming.

Answer 1

Heya !!!

Here is Your answer.

(While preparing for my examination, I got a formula and I was eager to share)

So, Let us continue....

As per the Question, we have to find 6 rational numbers between 5 and 7.

Using the formula which I have, you can find any number of rational numbers between two rational numbers, upto n numbers.

Formula :-
$a + \frac{n(b - a)}{n + 1}$
Where, a and b are two rational numbers and n = 1, 2, 3, ....., n.

So, Let us solve out...
a = 5 and b = 7.

First...
$5+ \frac{1(7- 5)}{1 + 1} \\ = 5 + \frac{2}{ 2 } = 6$

Second...
$5+ \frac{2(7 - 5)}{2 + 1} \\ = 5 + \frac{4}{3} = \frac{19}{3}$

Third....
$5+ \frac{3(7 - 5)}{3+ 1} \\ = 5 + \frac{6}{4} \\ = 5 + \frac{3}{2} = \frac{13}{2}$
Putting, n = 4, 5, 6 and so on.

we can get any number of rational numbers.

Hope It Helps

Answer 2

Answer:-

(1) 6

(2) 11/2

(3) 21/4

(4) 41/8

(5) 81/16

(6) 161/32